<title>Estimation of motion parameters by isolating scatterers using time-frequency filtering</title>

Multicomponent Doppler-coupled radar echoes, frequently encountered in detecting composite targets like near-space hypersonic vehicles, induce severe distortions in one-dimensional range profiles, including peak shifts and false targets. To address this, this paper proposes a method integrating the Discrete Polynomial Phase Transform (DPT) with Singular Value Decomposition (SVD) for echo decoupling and range profile correction. The core procedure begins by converting the echoes into constant-frequency monocomponent signals via DPT, which enables precise Time of Arrival (TOA) estimation using a cross-correlation algorithm. Following this, the Doppler frequency is extracted through dechirping. Subsequently, SVD is employed to separate the individual signal components, each of which then undergoes Doppler compensation to reconstruct a final, corrected range profile. Comprehensive simulations demonstrate the method's superior performance. At a 0 dB signal-to-noise ratio (SNR), it reduces the relative residual power in the compensated range profile to below −25 dB and achieves a target range error probability exceeding 90% within ±2 range resolution cells. These quantitative results, along with favorable comparisons against established benchmarks in TOA estimation accuracy and false target suppression, conclusively validate the effectiveness and superiority of the proposed approach for processing multicomponent Doppler-coupled echoes.

HighlightsWhat are the main findings?This paper presents a high-order phase compensation and parameter estimation algorithm designed for maneuvering targets, which effectively balances detection performance and computational efficiency.The proposed method achieves precise compensation of high-order range migrations without the need for exhaustive parameter search, thereby circumventing the blind speed sidelobe effect. Futhermore, the incorporation of a time-delay variable significantly improves the anti-noise capability of the approach.What is the implication of the main finding?This algorithm introduces a novel motion compensation technique to address the challenges of range migration, Doppler frequency migration, and Doppler ambiguity in detecting weak maneuvering targets. It achieves precise range migration compensation with enhanced accuracy and robustness, forming a vital preprocessing step for high-quality SAR imaging.The algorithm supports simultaneous multi-target processing and holds promising application potential in fields such as airborne radar detection, maritime moving target indication, cooperative observation by UAV formations, and other fields.This study focuses on the key challenges in detecting and estimating motion parameters of ground maneuvering targets for airborne radar sensors. The complex unknown motion states of the ground maneuvering target, including velocity, acceleration, and jerk, result in range migrations (RMs) and Doppler frequency migrations (DFMs). These effects severely degrade the long-time coherent accumulation performance of the airborne radar, thereby limiting the reliable detection and precise parameter estimation of maneuvering targets. To address this issue, a new detection and motion parameter estimation method based on the range frequency reversal transform (RFRT) and searching Lv’s distribution (SLVD), i.e., RFRT-SLVD, is proposed. Specifically, the third-order RM (TRM) and quadratic DFM (QDFM) are considered. The proposed method operates as follows: First, RMs are eliminated simultaneously via the RFRT operation, which multiplies the echo by its reversed data in the range frequency and slow-time domains, leveraging the symmetric equal-interval sampling property of the range frequency. Subsequently, a phase compensation function (PCF) related to the jerk is constructed to compensate the QDFM. Finally, the LVD is performed to remove residual DFMs and achieve effective signal energy accumulation. Additionally, the case of a fast-moving target with Doppler ambiguity is analyzed, and a method for estimating three motion parameters is provided. A key advantage of the proposed technique is its ability to directly compensate the RMs without requiring prior knowledge of the maneuvering target, while also avoiding the blind speed sidelobe (BSSL) effect. In comparison with existing algorithms, RFRT-SLVD achieves a balanced trade-off between parameter estimation performance and computational efficiency. Numerical analyses and experiments are conducted to validate the method, assessing its detection capability for ground maneuvering targets, Doppler ambiguity resolution in parameter estimation, computational complexity, and method applicability in multi-target scenarios.

In most applications, component extraction is important when components of non-stationary multi-component signal are key features to be monitored and analyzed. Existing methods are either sensitive to noise or forced to select a proper time-frequency representation for the considered signal. In this paper, we present a novel component extraction method for non-stationary multi-component signal. The proposed method combines parameterized de-chirping and band-pass filter to obtain components of multi-component signal, which avoids dealing with time-frequency representation of the signal and works well under heavy noise. In addition, it is able to analyze the multi-component signal whose components have intersected instantaneous frequency trajectories. Simulation results show that the proposed method is promising in analyzing complicated multi-component signals. Moreover, it works effective in a high noise environment in terms of improving the output signal-to-noise rate for the interested component.

A fast ground moving target focusing method based on first-order discrete polynomial-phase transform

The components in an engineering signal may overlap in the frequency domain, which causes great inconvenience and even errors in traditional one-dimensional signal processing methods. To identify and extract components in the signal from the time-frequency domain, this paper proposes a time-frequency domain signal decomposition method based on enhanced seeded region growing (ESRG). This paper extends the seeded region growing method to adaptive recognition of target regions in the time-frequency representation and divides the time-frequency representation into several time-frequency components. ESRG can reduce the influence of noise, expand the self-adaptability of time-frequency decomposition and avoid errors caused by manually setting the growth point and threshold. The results of the numerical verification and decomposition of bat echo signals show that this method can accurately decompose multi-component non-stationary signals. The decomposition results of rotor fault and rolling bearing fault signals show that this method can be successfully applied to fault diagnosis.

An efficient method for parameter estimation and separation of multi-component LFM signals

Tradicionalmente, la detección de faltas en máquinas eléctricas se basa en el uso de la Transformada Rápida de Fourier ya que la mayoría de las faltas pueden ser diagnosticadas con ella con seguridad si las máquinas operan en condiciones de régimen estacionario durante un intervalo de tiempo razonable.
\nSin embargo, para aplicaciones en las que las máquinas operan en condiciones de carga y velocidad fluctuantes (condiciones no estacionarias) como por ejemplo los aerogeneradores, el uso de la Transformada Rápida de Fourier debe ser reemplazado por otras técnicas.
\nLa presente tesis desarrolla una nueva metodología para el diagnóstico de máquinas de inducción de rotor de jaula y rotor bobinado operando en condiciones no estacionarias, basada en el análisis de las componentes de falta de las corrientes en el plano deslizamiento frecuencia. La técnica es aplicada al diagnóstico de asimetrías estatóricas, rotóricas y también para la falta de excentricidad mixta.
\nEl diagnóstico de las máquinas eléctricas en el dominio deslizamiento-frecuencia confiere un carácter universal a la metodología ya que puede diagnosticar máquinas eléctricas independientemente de sus características, del modo en el que la velocidad de la máquina varía y de su modo de funcionamiento (motor o generador).
\nEl desarrollo de la metodología conlleva las siguientes etapas:
\n(i) Caracterización de las evoluciones de las componentes de falta de asimetría estatórica, rotórica y excentricidad mixta para las máquinas de inducción de rotores de jaula y bobinados en función de la velocidad (deslizamiento) y la frecuencia de alimentación de la red a la que está conectada la máquina.
\n(ii) Debido a la importancia del procesado de la señal, se realiza una introducción a los conceptos básicos del procesado de señal antes de centrarse en las técnicas actuales de procesado de señal para el diagnóstico de máquinas eléctricas.
\n(iii) La extracción de las componentes de falta se lleva a cabo a través de tres técnicas de filtrado diferentes: filtros basados en la Transformada Discreta Wavelet, en la Transformada Wavelet Packet y con una nueva técnica de filtrado propuesta en esta tesis, el Filtrado Espectral. Las dos primeras técnicas de filtrado extraen las componentes de falta en el dominio del tiempo mientras que la nueva técnica de filtrado realiza la extracción en el dominio de la frecuencia.
\n(iv) La extracción de las componentes de falta, en algunos casos, conlleva el desplazamiento de la frecuencia de las componentes de falta. El desplazamiento de la frecuencia se realiza a través de dos técnicas: el Teorema del Desplazamiento de la Frecuencia y la Transformada Hilbert.
\n(v) A diferencia de otras técnicas ya desarrolladas, la metodología propuesta no se basa exclusivamente en el cálculo de la energía de la componente de falta sino que también estudia la evolución de la frecuencia instantánea de ellas, calculándola a través de dos técnicas diferentes (la Transformada Hilbert y el operador Teager-Kaiser), frente al deslizamiento. La representación de la frecuencia instantánea frente al deslizamiento elimina la posibilidad de diagnósticos falsos positivos mejorando la precisión y la calidad del diagnóstico. Además, la representación de la frecuencia instantánea frente al deslizamiento permite realizar diagnósticos cualitativos que son rápidos y requieren bajos requisitos computacionales.
\n(vi) Finalmente, debido a la importancia de la automatización de los procesos industriales y para evitar la posible divergencia presente en el diagnóstico cualitativo, tres parámetros objetivos de diagnóstico son desarrollados: el parámetro de la energía, el coeficiente de similitud y los parámetros de regresión. El parámetro de la energía cuantifica la severidad de la falta según su valor y es calculado en el dominio del tiempo y en el dominio de la frecuencia (consecuencia de la extracción de las componentes de falta en el dominio de la frecuencia). El coeficiente de similitud y los parámetros de regresión son parámetros objetivos que permiten descartar diagnósticos falsos positivos aumentando la robustez de la metodología propuesta.
\nLa metodología de diagnóstico propuesta se valida experimentalmente para las faltas de asimetría estatórica y rotórica y para el fallo de excentricidad mixta en máquinas de inducción de rotor de jaula y rotor bobinado alimentadas desde la red eléctrica y desde convertidores de frecuencia en condiciones no estacionarias estocásticas.

In this paper, we are interested in the problem of parameter estimation of 3-order polynomial phase signals (PPS) affected by additive Gaussian white noise. A new algorithm for 3-order PPS parameter estimation is proposed. Filter bank, short time Radon-Wigner transform, cure fitting and local scope searching algorithm is adopt together to get the parameter's accurate estimation. The merit of this new algorithm is validated by illustrative examples in low (SNR) condition.

High-resolution methods are generally defined to be high-performance methods for estimating and/or detecting the desired and/or undesired signal components present in a given set of data. The term “high-resolution” also implies a good ability to resolve very “similar” signal components. One of the most common problems in signal processing is known as frequency estimation. In frequency estimation, “high-resolution” often refers to a good ability to resolve two or more closely located frequencies in the given data. There are two groups of high-resolution methods. One is parametric methods, and the other non-parametric methods. The parametric high-resolution methods result from ingenious exploitations of known data structures. The non-parametric high-resolution methods maximize the output of some desired information with little knowledge of the data structure. The choice between parametric methods and non-parametric methods largely depends on one’s confidence in the assumed data model. In this chapter, we expose the readers to a range of existing parametric high-resolution methods. In Section 1.2, we present several frequency estimation techniques using algebraic principles. They are linear prediction, matrix pencil, and iterative quadratic maximum likelihood. The linear prediction method and the matrix pencil method can achieve near-optimal accuracy of estimation without the local convergence issues associated with the optimal methods. The computational complexities of the two methods are among the most efficient. The iterative quadratic maximum likelihood method is an approximation of the (exact) maximum likelihood method. Under some condition (e.g., high SNR), this approximation achieves the optimal accuracy. Concepts like forwardand-backward averaging, total least square, and (joint) singular value decomposition of orthonormal matrices will also be discussed. In Section 1.3, we present methods that exploit large sample theorems in statistics. In particular, we focus on data of multiple independent measurements. The key data structure is captured by the dominant (principal) subspace of the data matrix or the dominant eigenvectors of the data covariance matrix. The principal subspace is referred

LFM signals are widely used in the fields of radar and communication etc., which make signals detection and parameters estimation a very important technology in multicomponent LFM signals. To solve the problems of error detection caused by the cross-terms in WVD-Hough methods and other modified WVD distribution methods, and low parameter estimation precision due to poor timefrequency concentration in S-Hough transform, this paper proposed a detection and parameter estimation algorithm of multicomponent LFM signals based on reassigned generalized S-transform and Hough transform. Firstly calculate the time-frequency distribution of multicomponent LFM signals by generalized S-transform. Secondly reassign the S-transform time-frequency distribution to improve the time-frequency concentration property. Finally implement signal detection and parameter estimation by Hough transform to the reassigned S-transform TFD. The simulation results show that this algorithm has good performance in detecting multicomponent LFM signals and estimating the parameters in low SNR case.

Nonlinear squeezing time–frequency transform for weak signal detection

In this thesis we address the problem of decomposing a signal containing multiple non-stationary sinusoids into its components. A non-stationary sinusoid is one whose envelope and frequency are functions of time; we assume that these variations are slow enough so that the components occupy distinct regions in the spectrum at each instant of time. We propose to separate the components by using moving bandpass filters. Each moving bandpass filter is implemented as a cascade of demodulator, low-pass filter, and remodulator. We use the instantaneous frequency of the assigned component for tracking. We point out that while the raw instantaneous frequency may be potentially misleading, its smoothed counterpart is physically very meaningful and can be reliably used for moving the filters. The burden on a filter to isolate its component is eased by subtracting from its input an estimate of other signal components. This is based on the principle of Residual Signal Analysis, originally proposed by Costas. Our procedure results in a cleaner separation of the components when compared with his implementation. We have also proposed a feedforward structure to carry out Residual Signal Analysis. Using these methods for voiced speech analysis we have found that the components need not necessarily be precisely harmonic but only nominally so, and that there can be brief periods of time when some of them can become significantly mistuned; the envelopes of some of the components displayed significant amplitude modulation. Teager has raised a number of objections against the popularly used source-filter model and has claimed that it is completely wrong. Our simulation results indicate that this model reproduces quite accurately the frequency mistuning seen in the examples of natural speech we have looked at. We also demonstrate that the polynomial envelope and phase model for non-stationary signal analysis is sensitive to model mismatch and does not automatically yield the increased accuracy expected of it. The recently proposed DESA-1a algorithm of Maragos, et al. is shown to be equivalent to Prony's method for the noiseless sinusoid case and an ad hoc variant of it in the presence of noise.

Instantaneous frequency (IF) estimation of multi-component signals with closely spaced and intersecting signal components of varying amplitudes is a challenging task. This paper presents a novel iterative time–frequency (TF) filtering approach to address this problem. The proposed algorithm first adopts a high-resolution time–frequency distribution to resolve close components in the TF domain. Then, IF of the strongest signal component is estimated by a new peak detection and tracking algorithm that takes into account both the amplitude and the direction of peaks in the TF domain. The estimated IF is used to remove the strongest component from the mixture, and this process is repeated till the IFs of all signal components are estimated. Experimental results show the superiority of the proposed method as compared to other state-of-the-art methods.

Investigation on drought characteristics such as severity, duration, and frequency is crucial for water resources planning and management in a river basin. While the methodology for multivariate drought frequency analysis is well established by applying the copulas, the estimation on the associated parameters by various parameter estimation methods and the effects on the obtained results have not yet been investigated. This research aims at conducting a comparative analysis between the maximum likelihood parametric and non-parametric method of the Kendall \(\tau \) estimation method for copulas parameter estimation. The methods were employed to study joint severity–duration probability and recurrence intervals in Karkheh River basin (southwest Iran) which is facing severe water-deficit problems. Daily streamflow data at three hydrological gauging stations (Tang Sazbon, Huleilan and Polchehr) near the Karkheh dam were used to draw flow duration curves (FDC) of these three stations. The \(Q_{75}\) index extracted from the FDC were set as threshold level to abstract drought characteristics such as drought duration and severity on the basis of the run theory. Drought duration and severity were separately modeled using the univariate probabilistic distributions and gamma–GEV, LN2–exponential, and LN2–gamma were selected as the best paired drought severity–duration inputs for copulas according to the Akaike Information Criteria (AIC), Kolmogorov–Smirnov and chi-square tests. Archimedean Clayton, Frank, and extreme value Gumbel copulas were employed to construct joint cumulative distribution functions (JCDF) of droughts for each station. Frank copula at Tang Sazbon and Gumbel at Huleilan and Polchehr stations were identified as the best copulas based on the performance evaluation criteria including AIC, BIC, log-likelihood and root mean square error (RMSE) values. Based on the RMSE values, nonparametric Kendall-\(\tau \) is preferred to the parametric maximum likelihood estimation method. The results showed greater drought return periods by the parametric ML method in comparison to the nonparametric Kendall \(\tau \) estimation method. The results also showed that stations located in tributaries (Huleilan and Polchehr) have close return periods, while the station along the main river (Tang Sazbon) has the smaller return periods for the drought events with identical drought duration and severity.

This paper addresses the issue of detection and parameter estimation of multicomponent Polynomial Phase Signals (mc-PPS’s) embedded in noise based on high-order ambiguity function (HAF). We first show how existing PHAF-based techniques (PHAF—product HAF) are inadequate mainly in providing reliable detection for mc-PPS. The main contribution of this paper is that we present a novel parameter estimation method. Firstly, given a set of time delay, it gives rise to a set of estimates of phase coefficients based on HAF. Then it produces a final estimate of phase coefficient by means of voting. The new method improves the probability of detection and estimation accuracy while avoiding the issue of threshold selection. Computer simulations are carried out to illustrate the advantage of the proposed method over existing techniques.